Blair Alston's second goal in two games gave Falkirk a point at Firhill.
Midfielder Alston side-footed a powerful villey past Scott Fox from the edge of the box on 72 minutes to level the scores.
Mark McGuigan had tapped Partick into a first half lead but as both teams toiled, the time of year was obvious as the season winds down to closure next week.
Falkirk were unorthodox, without the exiled Willie Gibson at number 10 and with Rhys Bennett and Stephen Kingsley on eiither side of the central defenders.
And it was down the left side, that Partick attacked, with Stephen O'Donnell causing great difficulty for Kingsley throughout the first 45 minutes.
The left-back contained his man better in the second half but it was through O'donnell Partick took the lead on 24 minutes. He hit the by-line and fired a low cross into the box which tangled in Paul Cairney's legs. Under pressure from Murray Wallace he stabbed it across goal for McGuigan to beat Darren Dods to the ball and knock in from close range.
Falkirk only had one chance to speak of in the first half, and Michael McGovern was the busier golakeeper, twice dealing with awkward pass -backs from Murray Wallace.
Farid El Alagui spurned Falkirk's chance on 16 minutes aiming for the corner of the net he fired a straight shot just wide from the edge of the box after Alston laid off Craig Sibbald's cross.
The visitors were forced into a change when David Weatherston injured his right hip and was replaced by Kris Faulds, and prompted a midfield reshuffle that pushed Alston and then Jay Fulton wide.
However the change didn't hurt ALston's performance and he nipped in front of Thistle captain Alan Archibald playing his 400th Jags game, to stroke the Bairns level from Sibbald's pass.
Falkirk will model their new season strip next week in the final match of the season against Ayr United at The Falkirk Stadium.
The Bairns can reach second place on goal difference if they win and Dundee lose.